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Numerade Educator

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Problem 3 Medium Difficulty

A variable force of $ 5x^{-2} $ pounds moves an object along a straight line when it is $ x $ feet from the origin. Calculate the work done in moving the object from $ x = 1 ft $ to $ = 10 ft $.

Answer

4.5 pound-feet

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Video Transcript

a variable force of five X two *** to power pounds moves an object along a straight line where it isthe ex feet frowned origin. Calculate the work dying moving object from X equal to one feet to x equal to ten feet. So for this problem, since it's not like on the first problem where it only give us like a pound and the total distance it's moving, it's giving us a range. Uh, so in this case now what we're going to do is we're going to introduce the formula. Their work is equal to the integration of two function of force the ex. So this is a function a force. Of course. DX kind of represents the distance, but it's actually we'LL get our distance after we integrated. So in this case, our hot functional force is given as five X to the native to power because it isthe value with pounds so we can just set it up. It's great five x to the native to power the ex. So how much are we moving? We're moving from one to ten feet, so now if we integrate that because it's too negative to power, so it will change your two x two nato one power hum. We will divide this by the power negative one. And don't forget our five. No, we're going Teo, integrate from one to ten and this will equal to five times ten to the negative one who are negative. One minus five times one to the NATO one over near one which will give us, um five over ten Negative fi over ten Negative negative will give us past five. So if we do some basic algebra here will get positive for point five and again our unit here is going to be pound feet.